2-local Lie isomorphisms of operator algebras on Banach spaces

Let $X$ and $Y$ be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism $\phi $ of $B(X)$ onto $B(Y)$ has the form $\phi =\varphi +\tau $, where $\varphi $ is an isomorphism or the negative of an anti-isomorphism o

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